Related papers: Linear Time Construction of Indexable Elastic Foun…
Indexing labeled graphs for pattern matching is a central challenge of pangenomics. Equi et al. (Algorithmica, 2022) developed the Elastic Founder Graph ($\mathsf{EFG}$) representing an alignment of $m$ sequences of length $n$, drawn from…
We study the problem of matching a string in a labeled graph. Previous research has shown that unless the Orthogonal Vectors Hypothesis (OVH) is false, one cannot solve this problem in strongly sub-quadratic time, nor index the graph in…
We introduce a compact pangenome representation based on an optimal segmentation concept that aims to reconstruct founder sequences from a multiple sequence alignment (MSA). Such founder sequences have the feature that each row of the MSA…
This paper shows the weighted matching problem on general graphs can be solved in time $O(n(m + n\log n))$ for $n$ and $m$ the number of vertices and edges, respectively. This was previously known only for bipartite graphs. The crux is a…
In this paper, we give new, tight subexponential lower bounds for a number of graph embedding problems. We introduce two related combinatorial problems, which we call String Crafting and Orthogonal Vector crafting, and show that these…
Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation graphs…
We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut…
The run time complexity of state-of-the-art inference algorithms in graph-based dependency parsing is super-linear in the number of input words (n). Recently, pruning algorithms for these models have shown to cut a large portion of the…
We revisit the complexity of approximate pattern matching in an elastic-degenerate string. Such a string is a sequence of $n$ finite sets of strings of total length $N$, and compactly describes a collection of strings obtained by first…
Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the given pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation…
Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe a randomized algorithm to preprocess the graph in O(gn log n) time…
For the first time we provide a succinct pattern matching index for arbitrary graphs that can be built in polynomial time, which requires less space and answers queries more efficiently than the one in [SODA 2021]. We show that, given an…
Missing data imputation (MDI) is crucial when dealing with tabular datasets across various domains. Autoencoders can be trained to reconstruct missing values, and graph autoencoders (GAE) can additionally consider similar patterns in the…
An elastic-degenerate (ED) string is a sequence of $n$ sets of strings of total length $N$, which was recently proposed to model a set of similar sequences. The ED string matching (EDSM) problem is to find all occurrences of a pattern of…
The directed acyclic word graph (DAWG) of a string $y$ of length $n$ is the smallest (partial) DFA which recognizes all suffixes of $y$ with only $O(n)$ nodes and edges. In this paper, we show how to construct the DAWG for the input string…
In the String Matching in Labeled Graphs (SMLG) problem, we need to determine whether a pattern string appears on a given labeled graph or a given automaton. Under the Orthogonal Vectors hypothesis, the SMLG problem cannot be solved in…
Message-passing neural networks (MPNNs) are the leading architecture for deep learning on graph-structured data, in large part due to their simplicity and scalability. Unfortunately, it was shown that these architectures are limited in…
We study the problem of finding maximal exact matches (MEMs) between a query string $Q$ and a labeled graph $G$. MEMs are an important class of seeds, often used in seed-chain-extend type of practical alignment methods because of their…
Let $G$ be an $n$-node and $m$-edge positively real-weighted undirected graph. For any given integer $f \ge 1$, we study the problem of designing a sparse \emph{f-edge-fault-tolerant} ($f$-EFT) $\sigma${\em -approximate single-source…
In this paper, we extend the notion of gapped strings to elastic-degenerate strings. An elastic-degenerate string can been seen as an ordered collection of k > 1 seeds (substrings/subpatterns) interleaved by elastic-degenerate symbols such…